Discrete breathers and Anderson modes: two faces of the same phenomenon?

Abstract

Time-periodic localized oscillations occur in a variety of contexts, in particular in weakly coupled anharmonic lattices and in disordered harmonic networks of oscillators, where they are known respectively as discrete breathers and Anderson modes. It is shown numerically in some examples of systems which interpolate between these two limits that discrete breathers can be continued to Anderson modes, modulo small jumps associated with resonance with Anderson modes on other parts of the network.